Ising model on directed small-world Voronoi Delaunay random lattices

Abstract: We investigate the critical properties of the Ising model in two dimensions on {\it directed} small-world lattice with quenched connectivity disorder. The disordered system is simulated by applying the Monte Carlo update heat bath algorithm. We calculate the critical temperature, as well as the critical exponents $\gamma/\nu$, $\beta/\nu$, and $1/\nu$ for several values of the rewiring probability $p$. We find that this disorder system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The Ising model on {\it directed} small-world lattices presents in fact a second-order phase transition with new critical exponents which do not dependent of $p$, but are identical to the exponents of the Ising model and the spin-1 Blume-Capel model on {\it directed} small-world network.